Mass flow meters utilizing the general principle of angular or linear momentum have been used in the past as disclosed by the following references.
______________________________________ U.S. Pat. No. Name Date ______________________________________ 1,401,299 Wohlenberg 12-21 2,804,771 Brown 09-57 3,049,919 Roth 08-62 3,206,978 Aronow 09-65 3,429,181 Shiba 02-69 3,538,769 Shiba 11-70 3,584,508 Shiba 06-71 3,693,437 Shiba 09-72 ______________________________________
These references disclose meters that accomplish mass flow measurements by application of the momentum equation over one or more control surfaces which are assumed to have a constant, or nearly constant, velocity profile for the flowing fluid over the entire control surface or surfaces of interest. The velocity profile of a flowing fluid in a mass flow meter is dependent upon many factors, such as conduit disturbances upstream of the meter, curvature of the fluid path within the meter or immediately upstream of the meter's inlet opening, roughness of the boundary material of the fluid path, heat transfer characteristics of the fluid and the meter's structure, viscosity of the fluid, Reynolds Number of the fluid, and so forth. The necessity of having a velocity profile of the flowing fluid as constant as possible at each control surface of interest has been recognized in the prior art (Wohlenberg No. 1,401,299), but the prior art does not teach the utilization of the meter's structure itself for establishing these constant velocity profiles. Usually, the condition of constant velocity over a control surface of interest, if addressed in the prior art, is accomplished by providing as ideal flow conditions as possible external to the meter. In some applications, providing ideal flow conditions external to the meter is not possibile or practicable.
The meters in the above references measure the mass or volumetric flow of a fluid passing through them based upon application of the momentum equation. An essential element of the momentum equation is evaluation of the surface integral: EQU F=.intg..intg..rho.V.multidot.(V.multidot.dA)
where F is the vector components of force being measured, .rho. is the scalar density of the flowing fluid, V is the velocity vector of the fluid measured relative to a control volume and dA is the differential surface area vector of the selected control volume. To accurately calculate F, it is essential to know the characteristics of the velocity vector at the control surface where the momentum equation is applied. Without utilizing structure in the meter itself, as in the present invention, which generates an essentially constant velocity profile of the flowing fluid at the control surface where the momentum equation is applied, there is no certainty of what the velocity profile will be at that surface area. If, however, a constant velocity of the flowing fluid can be established over the control surface, the one-dimensional momentum equation applied over this surface area reduces to:
ti F=.rho.V.sup.2 A
assuming .rho. is constant. If the specific value of .rho. is unknown, it can be determined by other means. Parameter A is known since it is the area of the control surface across which the fluid flows. Parameter F is determined by measurement. Therefore, parameter V, the velocity of the fluid, can be solved for as the only unknown in the above equation as: ##EQU1## Mass flow rate, Q, can then be determined from the following equation: EQU Q=.rho.VA
The necessity of establishing a constant velocity profile of the flowing fluid when attempting to accurately measure flow by means of the momentum equation can be illustrated by examining the effects of flowing fluids with non-constant velocities on the momentum equation. FIG. 1 shows several fluid velocity profiles, each with the same mass flow rate. Velocity profiles of power law fluids were derived from equations presented on page 7-16 of Handbook of Fluid Dynamics by V. L. Streeter, 1961 edition. The force component, F, attributable to each of these profiles will be different and increasing in value when going from the constant velocity profile in FIG. 1(a) to the triangular velocity profile of FIG. 1(f), with corresponding difference in measurement of mass flow rate, Q, of approximately 22.5 percent when using the previously defined formulas. Therefore, unless the exact velocity profile of the flowing fluid is known for all flow conditions, a mass flow meter will be susceptible to large errors in flow measurement. The best method of knowing the exact velocity profile is to use a meter which establishes a constant velocity profile for all measurements, as is done by the present invention.
Wohlenberg U.S. Pat. No. 1,401,299, Brown U.S. Pat. No. 2,804,771, Roth U.S. Pat. No. 3,049,919 and Shiba U.S. Pat. No. 3,584,508 teach U-shaped mass flow meters which in general are dependent upon the velocity profiles at a minimum of two control surfaces (i.e., inlet and outlet openings). The present invention is dependent upon a minimum of one velocity profile (i.e., outlet opening). Aronow U.S. Pat. No. 3,206,978 teaches a meter with only one control surface, but does not attempt to control the velocity profile across that surface. Shiba U.S. Pat. No. 3,429,181 teaches a cup type mass flow meter but does not attempt to control velocity profile over the control surface. Shiba U.S. Pat. No. 3,538,769 teaches mainly flow meters which measure mass flow with angular momentum measurements, as opposed to linear momentum measurements. Shiba U.S. Pat. No. 3,693,437 teaches a one dimensional flow meter, as the present invention, but utilizes a Venturi tube and effect, and two control surfaces, without stucture for establishing constant velocity profiles of the flowing fluid.